Әділ бөлу мәселесі және ресурстарды тағайындау

Problem of sharing resources
Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. That problem arises in various real world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth observation satellites. It is an active research area in mathematics, economics (especially social choice theory), dispute resolution, etc. The central tenet of fair division is that such a division should be performed by the players themselves, maybe using a mediator but certainly not an arbiter as only the players really know how they value the goods. The archetypal fair division algorithm is divide and choose. It demonstrates that two agents with different tastes can divide a cake such that each of them believes that he got the best piece. The research in fair division can be seen as an extension of this procedure to various more complex settings. There are many different kinds of fair division problems, depending on the nature of goods to divide, the criteria for fairness, the nature of the players and their preferences, and other criteria for evaluating the quality of the division.

In addition to fairness, it is sometimes desired that the division be Pareto optimal, i. e., no other allocation would make someone better off without making someone else worse off. The term efficiency comes from the economics idea of the efficient market. A division where one player gets everything is optimal by this definition so on its own this does not guarantee even a fair share. See also efficient cake cutting and the price of fairness. In the real world people sometimes have a very accurate idea of how the other players value the goods and they may care very much about it. The case where they have complete knowledge of each other's valuations can be modeled by game theory. Partial knowledge is very hard to model. A major part of the practical side of fair division is the devising and study of procedures that work well despite such partial knowledge or small mistakes. An additional requirement is that the fair division procedure be a truthful mechanism, i. e., it should be a dominant strategy for the participants to report their true valuations. This requirement is usually very hard to satisfy in combination with fairness and Pareto efficiency.

Recently, the model of fair division has been extended from individual agents to families (pre determined groups) of agents. See Fair division among groups.

The 17 animal inheritance puzzle involves the fair division of 17 camels (or elephants, or horses) into the proportions 1/2, 1/3, and 1/9. It is a popular mathematical puzzle, often claimed to have an ancient origin, but its first documented publication was in 18th century Iran. In Numb3rs season 3 episode "One Hour", Charlie talks about the cake cutting problem as applied to the amount of money a kidnapper was demanding. Hugo Steinhaus wrote about a number of variants of fair division in his book Mathematical Snapshots. In his book he says a special three person version of fair division was devised by G. Krochmainy in Berdechów in 1944 and another by Mrs L Kott. Martin Gardner and Ian Stewart have both published books with sections about the problem. Martin Gardner introduced the chore division form of the problem. Ian Stewart has popularized the fair division problem with his articles in Scientific American and New Scientist. A Dinosaur Comics strip is based on the cake cutting problem. In the Israeli movie Saint Clara, a Russian immigrant asks an Israeli math teacher, how a circular cake can be divided fairly among 7 people? His answer is to make 3 straight cuts through its middle, making 8 equal pieces. Since there are only 7 people, one piece should be discarded, in the spirit of communism.

Vincent P. Crawford (1987). "fair division," The New Palgrave: A Dictionary of Economics, v. 2, pp. 274–75. Hal Varian (1987). "fairness," The New Palgrave: A Dictionary of Economics, v. 2, pp. 275–76. Bryan Skyrms (1996). The Evolution of the Social Contract Cambridge University Press. , chapters 11–13. Fair Division by Christian Klamler – in Handbook of Group Decision and Negotiation pp 183–202. Cake Cutting: Fair Division of Divisible Goods by Claudia Lindner and Jörg Rothe – in Economics and Computation pp 395–491. Fair division of indivisible goods by Jérôme Lang and Jörg Rothe – in Economics and Computation pp 493–550.